This invention relates to a method for measuring the resistivity of contacts on photovoltaic cells, and more particularly to a method for measuring contact resistivity of collector grid contacts using isolated segments of grid lines for contact end resistance and transmission line model measurements.
Measurement of contact resistance R.sub.c is of increasing importance in two semiconductor technologies: integrated circuits (IC) and photovoltaics (PV). The sizes of IC device features are continually decreasing, which causes an increase in the resistance of the conductor/semiconductor interface. A contact resistance R.sub.c of less than 10.sup.-6 ohm-cm.sup.2 is now desirable for very large scale integration(VLSI) applications. The practice is to produce a test pattern at some unused area of the VLSI. Conventional tests are then conducted to determine the parameters of the VLSI for quality control without affecting the operational circuit pattern.
Most PV manufacturers have not yet had to be concerned about contact resistance. Photovoltaic devices using crystalline silicon typically have contact resistance losses of less than 0.01% of the generated power. For nonconcentrating solar power applications, this loss is acceptable. However, if a PV concentrator cell is working at a 100-sun level, a change in the contact resistance can cause an appreciable power loss. Similarly, if the contact resistance of conductive coatings or metallizations on thin-film PV devices is too high, or changes with time, contact resistance can have important research and development implications. As a result of this increased interest, the various contact resistance measurement methods used for semiconductors have been examined.
Contact resistance can be measured by either ac or dc methods. Because ac methods introduce detrimental parasitic influences and, in common with dc measurement, require determination of small voltages or small voltage differences, only dc measurement techniques are of real interest. H. H. Berger reviewed the dc contact resistance measurement techniques in a paper titled "Contact Resistance and Contact Resistivity," J. Electrochem. Soc., Vol. 119, No. 4, pp 506-513, 1972. At that time he listed five different methods: twin contact, differential, extrapolation, interface probing and transmission line model (TLM). The analyses done by Berger showed that the differential, interface probing, and TLM approaches were potentially the three best. All three methods require specialized sample structures, although it is shown below that the TLM method can obviate this by use of modified portions of the standard PV-device grid-line metallization. Berger and others have improved on the TLM method.
More recently a direct contact resistance (DCR) measurement method was proposed by Proctor and Linholm in a paper titled "A Direct Measurement of Interfacial Contact Resistance," Electron. Device Letters, EDL-3 No. 5, May 1982, pp 294-296. This direct method has potential application in IC and PV research and development. However, the direct method requires three photolithographic steps to prepare a sample. This is a serious limitation when investigating samples of production crystalline PV devices. DCR measurement on many proposed thin-film PV devices would be impossible due to lack of a diffused layer. For these reasons, a different measurement approach is required for PV devices.
In all of the TLM approaches it is necessary to account for the effect of contact end resistance, R.sub.E. This effect was noted by Berger, supra. Later work reported by Harrison in a paper titled "Characterising Metal Semiconductor OHMIC Contacts," Proc. IREE Aust., pp 95-100, used the contact end resistance measurement and the contact resistance measurement to determine the attenuation constant for electrically short contacts. Subsequent work by Reeves and Harrison, reported in a paper titled "Obtaining the Specific Contact Resistance from Transmission Line Model Measurements," Electron. Device Lett., EDL-3 No. 5, May 1982, pp 111-113, extended the utility of contact end resistance measurement to the determination of modifications in sheet resistivity under contacts due to the alloying/sintering process.
The literature does not disclose any physical explanation for the phenomenon of contact end resistance. The best definition is by Harrison, supra: "R.sub.E is defined as the ratio of the contact output voltage V(d) to the contact input current I(o) when the contact output current is zero." While this definition is accurate, it does not provide a basis for understanding the phenomenon.
In a paper titled "Ohmic Contacts for VLSI Device Applications," Conf. on Microelectronics, Adelaide, Australia 12-14 May 1982, Reeves and Harrison showed a schematic representation of the various resistances found when measuring resistances of contacts. A similar representation is included here as FIG. 1. This shows where the contact end resistance may be found. Another view of a contact by Reeves and Harrison, and earlier by Berger in a paper titled "Contact Resistance on Diffused Resistors," Dig. Techn. Papers, 1969 IEE International Solid-State Circuit Conference (ISSCC) pp 160, 161, contains lines representing current flow and flux as shown in FIG. 2 herein.
The important concept here is the reduction of current flux across the metal-semiconductor interface as a function of distance from the leading edge of the contact. According to convention, the nature of a contact changes from an electrically short contact to an electrically long contact according to the following relationship: EQU d.gtoreq.2/.alpha. (1)
where:
d=contact length, cm PA1 .alpha.=attenuation constant, cm.sup.-1 PA1 R.sub.sk =sheet resistance under the contact, .OMEGA./.quadrature. PA1 .rho..sub.c =contact resistivity, .OMEGA.-cm.sup.2 PA1 R.sub.c =contact resistance, .OMEGA. PA1 R.sub.E =contact end resistance, .OMEGA. PA1 R.sub.sk =sheet resistivity under the contact, .OMEGA./.quadrature. PA1 .rho..sub.c =contact resistivity , .OMEGA.-cm.sup.2 PA1 d=width of collector grid line, cm PA1 w=length of segment of collector grid line, cm PA1 L.sub.1, L.sub.2 =line-to-line distances, cm
The attenuation constant is defined by: EQU .alpha.=(R.sub.sk /.rho..sub.c).sup.1/2 ( 2)
where:
If the electrically short contact (.alpha.d&lt;2) is visualized as a combination of a high contact resistance R.sub.c and a low sheet resistance R.sub.sk under the contact, then some of the current between contact 1 and contact 2 in FIG. 1 will have to flow through the conductor/semiconductor interface at the right edge of contact 2. A voltage measurement between contact 2 and contact 3 will include the interface at the right edge of contact 2 and thus there will be a voltage between contacts 2 and 3 due to a portion of the current between contacts 1 and 2. That voltage is a measurement of contact end resistance R.sub.E for contact 2. If the contact is electrically long (.alpha.d.gtoreq.2), then there will be little or no current flow across the interface at the right edge of contact 2 and therefore a very small, or no, contact end resistance, R.sub.E, measured. The equations for contact resistance and contact end resistance from Berger, J. Electrochem. Soc., Vol. 119, No. 4, pp 506-513, 1972, have been reformulated as: EQU R.sub.c =(R.sub.sk .rho..sub.c).sup.1/2 /(w tan h [d(R.sub.sk /.rho..sub.c).sup.1/2 ]) (3) EQU R.sub.E =(R.sub.sk .rho..sub.c).sup.1/2 /(W sin h [d(R.sub.sk /.rho..sub.c).sup.1/2 ]) (4)
where:
Equations (3) and (4) show that contact resistance is dependent upon both the quality of the contact and the modification of the semiconductor surface due to application of the contact. Work by Reeves and Harison, Electron. Device Lett., EDL-3, No. 5, May 1982, pp 111-113 has shown that the sheet resistance of a lightly doped silicon surface (R.sub.s =2100 .OMEGA./.quadrature.) may change by a factor of 5 while a gallium arsenide surface may change by a factor of 20 when metal is applied by alloying or sintering. Heavily doped silicon (R.sub.s =40 .OMEGA./.quadrature.), however, should change very little due to metallization sintering since it is already degenerate. This fact allows the substitution of a measured sheet resistance, R.sub.s, value for the sheet resistivity under the contact, R.sub.sk, for most present production solar cells. For gallium arsenide or other compound semiconductors, if modification of the sheet resistivity due to contact application can be shown to be predictable, then the modified value can be used. This substitution should not affect process control inspection since the determination of contact resistivity of poor contacts (using .rho..sub.c .ltoreq.1.times.10.sup.-3 .OMEGA.-cm.sup.2 as a definition of a good contact) is relatively insensitive to sheet resistivity values. This relationship is illustrated in FIG. 3.
Most contact resistance measurements for process control are made by using the TLM method along with a contact end resistance measurement. The TLM measurement relies upon a special pattern of three unequally spaced parallel contacts and the following equations from Berger, J. Electrochem. Soc., Vol. 119 No. 4, pp 506-513, 1972: ##EQU1## where: R.sub.1, R.sub.2 =measured resistance values, .OMEGA.
Note that since most PV cells have equally spaced grid lines for optimum device performance, the TLM approach cannot be used without modification of the grid lines because the denominator of equations (5) and (6) becomes zero.